Question

How do you solve `- x+y=6` and `-2x+y=7` using matrices?

Answer 1

`x=-1, y=5`

Explanation:

As the equations are already in the form `Ax+By=C`, writing all the coefficients of each equation to form each row of the matrix as below
`M=` `[(-1,1,|,6),(-2,1,|,7)]`
Now by row operations change `2xx2` matrix on the left side to identity matrix.

`M=` `[(1,0,|,-1),(-2,1,|,7)]`
Changed row 1 By subtracting row 2 from row 1

`M=` `[(1,0,|,-1),(0,1,|,5)]`
Changed row 2 By adding 2 `xx`row 1 to row 2

From right column we obtain the solution as

`x=-1, y=5`